Capacitive displacement gauges are known in the art. For most uses of such equipment, a probe of the capacitive displacement gauge is placed in close proximity to a target so that the area of the probe is parallel to the target. Changes in capacitance between the probe and target that result from any change in distance between the probe and the target are converted into an electrical signal that is utilized in order to accurately measure the change in distance between the probe and the target. It is most convenient to drive a capacitive displacement sensor with a constant current so that the sensor's output (in this case, the capacitor voltage) is a linear function of the distance between the probe and the target being measured by the gauge.
The open-loop gain of the capacitive displacement gauge is directly proportional to the probe capacitance, C.sub..rho.. Since the probe operates over some distance range the loop gain of the gauge will change as the probe-to-target distance changes. The distance ratio will produce a capacitance ratio of the same magnitude.
The changing loop gain of the gauge causes an undesirable change in the frequency response of the loop. At the crossover frequency (or gain-bandwidth product) of the loop, defined as the frequency at which the magnitude of the loop gain equals 1, the slope of the loop gain's rolloff must be less than 40 dB/decade. For a typical distance ratio of 4:1, a loop with a 20 dB/decade rolloff would exhibit a 4:1 change in frequency response; for a loop with a 40 dB/decade rolloff, the frequency would change by 2:1. This change in frequency is undesirable.
It would be desirable to have a device with a nonlinear transfer function such that the change in frequency response due to the changing loop gain of the probe which results from the change in distance between the probe and the target is avoided. Such a device would need to have a gain that varied as a function of its input so as to compensate for the change in gain caused by the variation in probe capacitance.